Chapter 11.1, Problem 47E

To determine

To determine: The correct option for the parameterizations of the unit circle will be traversed clockwise.

(A) $x=\cos t$ , $y=\sin t$ , $0\le t\le 2\pi$

(B) $x=\sin t$ , $y=\cos t$ , $0\le t\le 2\pi$

(C) $x=-\cos t$ , $y=-\sin t$ , $0\le t\le 2\pi$

(D) $x=-\sin t$ , $y=\cos t$ , $0\le t\le 2\pi$

(E) $x=\sin t$ , $y=-\cos t$ , $0\le t\le 2\pi$

Answer to Problem 47E

The correct option is (B).

Explanation of Solution

Calculation:

The parametric equations of a unit circle is $x=\sin t$ , $y=\cos t$ ; $0\le t\le 2\pi$

Now, for different values of t in different quadrants we get the following results as:

x moves 0 to 1 and y moves 1 to 0 in the interval $0\le t\le \frac{\pi }{2}$ .

x moves 1 to 0 and y moves 0 to $-1$ in the interval $\frac{\pi }{2}\le t\le \pi$ .

x moves 0 to $-1$ and y moves $-1$ to 0 in the interval $\pi \le t\le \frac{3\pi }{2}$ .

x moves $-1$ to 0 and y moves 0 to 1 in the interval $\frac{3\pi }{2}\le t\le 2\pi$ .

It is seen that the circle will traverse clockwise in this fashion.

Hence, the correct option is (B).